Explicit correlation and intermolecular interactions: investigating carbon dioxide complexes with the CCSD(T)-F12 method.

Abstract

We have optimized the lowest energy structures and calculated interaction energies for the CO(2)-Ar, CO(2)-N(2), CO(2)-CO, CO(2)-H(2)O, and CO(2)-NH(3) dimers with the recently developed explicitly correlated coupled cluster singles doubles and perturbative triples [CCSD(T)]-F12 methods and the associated VXZ-F12 (where X = D,T,Q) basis sets. For a given cardinal number, we find that results obtained with the CCSD(T)-F12 methods are much closer to the CCSD(T) complete basis set limit than the conventional CCSD(T) results. The relatively modest increase in the computational cost between explicit and conventional CCSD(T) is more than compensated for by the impressive accuracy of the CCSD(T)-F12 method. We recommend use of the CCSD(T)-F12 methods in combination with the VXZ-F12 basis sets for the accurate determination of equilibrium geometries and interaction energies of weakly bound electron donor acceptor complexes.

Full text

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THE JOURNAL OF CHEMICAL PHYSICS 134, 034301 (2011)
Explicit correlation and intermolecular interactions: Investigating carbon
dioxide complexes with the CCSD(T)-F12 method
Katrina M. de Lange and Joseph R. Lanea)
Department of Chemistry, University of Waikato, Private Bag 3105, Hamilton, New Zealand
(Received 7 October 2010; accepted 23 November 2010; published online 18 January 2011)
We have optimized the lowest energy structures and calculated interaction energies for the CO2–Ar,
CO2–N2, CO2–CO, CO2–H2O, and CO2–NH3dimers with the recently developed explicitly cor-
related coupled cluster singles doubles and perturbative triples [CCSD(T)]-F12 methods and the
associated VXZ-F12 (where X = D,T,Q) basis sets. For a given cardinal number, we find that results
obtained with the CCSD(T)-F12 methods are much closer to the CCSD(T) complete basis set limit
than the conventional CCSD(T) results. The relatively modest increase in the computational cost be-
tween explicit and conventional CCSD(T) is more than compensated for by the impressive accuracy
of the CCSD(T)-F12 method. We recommend use of the CCSD(T)-F12 methods in combination with
the VXZ-F12 basis sets for the accurate determination of equilibrium geometries and interaction en-
ergies of weakly bound electron donor acceptor complexes. © 2011 American Institute of Physics.
[doi:10.1063/1.3526956]
I. INTRODUCTION
The painfully slow convergence of electron correlation
energy with increasing basis set size is considered one of
the great challenges in modern computational chemistry. In
the last few years, significant advancements have been made
to accelerate this convergence by including a small number
of terms to the wavefunction that depend explicitly on the
interelectronic distance r12.1–4These so-called explicitly
correlated methods have been shown to give correlation
energies using a triple-ζ basis set that are better than conven-
tional coupled cluster singles doubles and perturbative triples
[CCSD(T)] with a quintuple-ζ basis set.5–8
Recently, we determined equilibrium geometries and in-
teraction energies for a series of hydrogen bonded complexes,
including H2O–H2O, H2O–H2S, H2O–NH3, and H2O–PH3,
withconventionalCCSD(T)andtheDunning-typecorrelation
consistent basis sets and with explicitly correlated CCSD(T)-
F12 and the corresponding VXZ-F12 (where X = D,T,Q)
basis sets.9We found that the CCSD(T)-F12 intermolec-
ular distances and interaction energies were in impressive
agreement with the CCSD(T) complete basis set (CBS) limit
and recommended use of this explicitly correlated method
for the accurate description of hydrogen bonded complexes.
This initial work9was restricted to relatively strong hydro-
gen bonded complexes, and so the conclusions drawn are
not necessarily generalizable to other types of more weakly
bound complexes that display different intermolecular in-
teractions. Recently, Marchetti et al. calculated CCSD(T)-
F12a interaction energies10for the S22 benchmark set of
complexes using the RI-MP2 geometries from the original
investigation.11
In the present investigation, we consider a series of
weakly bound complexes involving carbon dioxide, namely
CO2–Ar, CO2–N2, CO2–CO, CO2–H2O, and CO2–NH3.
a)Electronic mail: jlane@waikato.ac.nz.
These complexes exhibit weak electron donor acceptor and
more general van der Waals-type intermolecular interactions
and hence are representative of more weakly bound com-
plexes. We investigate the optimized geometries, harmonic
vibrational frequencies, and interaction energies for CO2–
Ar, CO2–N2, CO2–CO, CO2–H2O, and CO2–NH3and their
constituent monomer with both conventional and explic-
itly correlated CCSD(T)–F12 theory. The related MP2-F12
explicitly correlated method has been recently found to ac-
celerate basis set convergence of interaction energies for a
series of weakly bound electron donor acceptor complexes
involving CO2and nitrogen-containing heterocycles.12With
exception of CO2–NH3, the lowest energy structure of each
complex possesses C2v symmetry, which allows benchmark
quality conventional CCSD(T) results to be calculated. We
compare intermolecular distances andinteractionenergies ob-
tained with both conventional CCSD(T) and explicitly corre-
lated CCSD(T)-F12 to the CCSD(T)/CBS limit and, where
possible, to experiment.
Results from this investigation are useful not only for the
purpose of assessing the accuracy of the recently developed
CCSD(T)-F12 methods but also provide high quality equi-
librium geometries and interaction energies for a series of
atmospherically relevant molecular complexes. The equilib-
rium constant of formation (keq) for a weakly bound complex
depends exponentially on the interaction energy (at a given
temperature). It follows that accurately determining the inter-
action energies of CO2–Ar, CO2–N2, CO2–CO, CO2–H2O,
and CO2–NH3is crucial in order to estimate their abundance
and potential role in the atmosphere.
II. THEORETICAL METHODS
We have fully optimized the geometries of CO2–Ar,
CO2–N2, CO2–CO, CO2–H2O, and CO2–NH3and their con-
stituent monomers with the CCSD(T) ab initio theory using
0021-9606/2011/134(3)/034301/9/$30.00© 2011 American Institute of Physics
134, 034301-1
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034301-2K. M. de Lange and J. R. Lane J. Chem. Phys. 134, 034301 (2011)
Dunning-type correlation consistent basis sets. The CCSD(T)
method is considered the “gold-standard” of modern elec-
tronic structure theory, and with a suitably large basis set it
has been shown to give accurate geometries of small sys-
tems that are in excellent agreement with experiment.13–15We
have used the aug-cc-pVXZ basis sets (where X = D,T,Q,5,6)
for hydrogen and all the first row elements and the aug-cc-
pV(X+d)Z basis sets (where X = D,T,Q,5,6) for the second
row element Ar.16–18For brevity, we refer to these basis sets
as AVXZ (where X = D,T,Q,5,6), whereby it is assumed that
Ar has the additional tight d basis functions. We have opti-
mized the geometry of the complexes using both a standard
optimization scheme and a full counterpoise (CP) corrected
optimization scheme to reduce the effects of basis set super-
position error (BSSE) on our optimized geometries.19
We have also optimized the geometries of CO2–Ar,
CO2–N2, CO2–CO, CO2–H2O, and CO2–NH3 and their
constituent monomers with the recently developed explic-
itly correlated CCSD(T)-F12 methods, as implemented in
MOLPRO 2009.1.6,20We have used the VXZ-F12 orbital
basis sets (where X = D,T,Q) of Peterson et al. that have
been specifically optimized for use with explicitly correlated
F12 methods.21For a given cardinal number, the VXZ-F12
basis sets have been designed to be of a similar size to
the equivalent aug-cc-pVXZ and aug-cc-pV(X+d)Z basis
sets but have fewer diffuse basis functions. Density fitting
approximations22,23were used in all explicitly correlated
calculations using the VXZ/JKFIT (where X = D,T,Q)
and the AVXZ/MP2FIT (where X = D,T,Q) auxiliary
basis sets.24,25We have used the resolution of the identity
(RI) auxiliary basis sets of Yousaf and Peterson for all RI
approximations.26The complementary auxiliary basis set
singles correction was applied in all explicitly correlated
calculations,6which substantially improves the accuracy of
the Hartree–Fock contributions, particularly, with smaller
orbital basis sets.10The diagonal, fixed amplitude 3C(FIX)
ansatz was used, which is orbital invariant, size consistent,
and free of geminal basis set superposition error.3,27,28
Two different approximations are available for solving
the CCSD(T)-F12 energies in MOLPRO 2009.1, denoted
CCSD(T)-F12a and CCSD(T)-F12b.8,23Unless specified
when we refer to CCSD(T)-F12 we mean both the CCSD(T)-
F12a and CCSD(T)-F12b methods. The default CCSD-F12
correlation factor (1/βe−βr12, where β = 1) was used in all
explicitly correlated calculations.
We have extrapolated the CCSD(T) energies to the CBS
limit with the following two parameter extrapolation for the
correlation energy
Ecorr
XY=X3Ecorr
where X and Y are the cardinal numbers of the two basis
sets and Ecorr
X
and Ecorr
Y
are the corresponding correlation
energies.29,30The extrapolated correlation energy, Ecorr
added to the Hartree–Fock energy obtained with the larger
basis set to give an estimate of the CCSD(T)/CBS limit
energy.
We estimate the intermolecular distance of CO2–
Ar, CO2–N2, CO2–CO, CO2–H2O, and CO2–NH3 at the
X
X3− Y3
− Y3Ecorr
Y
,
(1)
XY, is
CCSD(T)/CBS limit by numerically determining the min-
imum of a CBS intermolecular potential obtained using
Eq. (1). The potential used extends from −0.40 to +0.50 Å
in 0.05 Å steps about the equilibrium value of either the stan-
dard optimized or CP optimized CCSD(T)/AV5Z intermolec-
ular distance. All other geometric parameters are kept fixed
at the corresponding CCSD(T)/AV5Z values. In principle, all
of the geometric parameters of the complexes could be opti-
mized at the CCSD(T)/CBS limit31but this is unfortunately
prohibitive with the AV5Z/AV6Z basis sets and our current
computational resources.
Unless specified all coupled cluster calculations assume
a frozen core (C:1s; N:1s; O:1s; Ar:1s,2s,2p) and were per-
formed using MOLPRO 2009.1.20The optimization thresh-
old criteria was set to gradient = 1× 10−6a.u., stepsize
= 1× 10−6a.u., and energy = 1× 10−8a.u. All single point
energies were converged to 1× 10−9a.u.
To confirm the nature of stationary points we calcu-
lated harmonic vibrational frequencies with conventional
CCSD(T), and the AVDZ and AVTZ basis sets and with
explicitly correlated CCSD(T)-F12 with the VDZ-F12 and
VTZ-F12 basis sets. These results are included in Tables
SI-SVI of the supplementary material.32For some of the
complexes with particularly flat potential energy surfaces,
we had difficulty in identifying true minima using numer-
ical second derivatives in MOLPRO 2009.1. Hence, we re-
optimized and calculated harmonic frequencies of CO2–Ar,
CO2–N2, CO2–CO, CO2–H2O, and CO2–NH3with conven-
tional CCSD(T)/AVTZ using the analytical gradients avail-
able in CFOUR.33The optimization and single point con-
vergence threshold criteria for these calculations were set
to SCF_CONV = 1× 10−10a.u., CC_CONV = 1× 10−11
a.u., LINEQ_CONV = 1× 10−11a.u., and GEO_CONV
= 1× 10−10a.u.
The intermolecular potential energy surface of a weakly
bound complex is highly anharmonic and hence ground
state vibrational averaging can signficantly increase the inter-
molecular distance from its equilibrium value (Re). We have
calculated the average intermolecular distance in the vibra-
tional ground state (Rg) and the intermolecular distance be-
tween average nuclei positions in the vibrational ground state
(Ra) using the ANHARM = VIBROT vibrational perturba-
tion routine in CFOUR.33The necessary cubic force constants
were evaluated with the CCSD(T)/AVTZ method.
To quantify the extent of charge transfer in the weakly
bound electron donor acceptor complexes, we have calcu-
lated atomic charges using the natural bond orbital analysis
in GAUSSIAN 09 (Ref. 34) and have included these in Table
SVII of the supplementary material.32For this analysis, we
have calculated single point CCSD/AVQZ energies obtained
at the CCSD(T)-F12b/VQZ-F12 optimized geometry.
III. RESULTS AND DISCUSSION
A. Monomer geometry
In Table I we present the geometric parameters of
N2, CO, CO2, H2O, and NH3optimized with the CCSD(T)
method and the explicitly correlated CCSD(T)-F12 methods
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034301-3 CCSD(T)-F12 intermolecular interactions J. Chem. Phys. 134, 034301 (2011)
TABLE I. Optimized geometric parameters (in angstrom and degrees) of N2, CO, CO2, H2O, and NH3.
N2
COCO2
H2O NH3
RNN
RCO
RCO
ROH
θHOH
RNH
θHNH
CCSD(T)
AVDZ
AVTZ
AVQZ
AV5Z
AV6Z
CBS
1.1209
1.1040
1.1005
1.0996
1.0993
1.0990
1.1473
1.1360
1.1318
1.1309
1.1306
1.1302
1.1775
1.1670
1.1631
1.1622
1.1620
1.1616
0.9665
0.9616
0.9590
0.9584
0.9584
0.9583
103.94
104.18
104.37
104.43
104.45
104.48
1.0237
1.0149
1.0128
1.0123
1.0122
1.0121
105.94
106.41
106.54
106.59
106.62
106.64
CCSD(T)-F12a
VDZ-F12
VTZ-F12
VQZ-F12
1.1000
1.0995
1.0990
1.1317
1.1309
1.1305
1.1630
1.1623
1.1618
0.9588
0.9588
0.9584
104.36
104.40
104.46
1.0123
1.0124
1.0121
106.59
106.59
106.64
CCSD(T)-F12b
VDZ-F12
VTZ-F12
VQZ-F12
1.0997
1.0993
1.0989
1.1310
1.1306
1.1303
1.1625
1.1620
1.1617
0.9585
0.9586
0.9583
104.34
104.40
104.45
1.0122
1.0124
1.0121
106.58
106.60
106.64
Expt.a
Expt.b
1.094
1.0977
1.1281
1.1284
1.1615
1.1601
0.958
0.9579
104.27
104.40
1.014
1.0139
106.47
107.17
aEquilibrium bond distances (Re) from Ref. 35.
bEquilibrium bond distances (Re) derived from experimental rotation constants using ab initio calculated vibration–rotation interaction constants from Ref. 39.
as well as the experimentally determined values. As expected,
the conventional CCSD(T) optimized geometric parameters
converge uniformlytowardtheCBSlimitasthecardinalnum-
ber of the basis set increases. We find that the bond lengths
progressively shorten and the bond angles steadily increase
from AVDZ to AV6Z. With the exception of the H2O and
NH3bond lengths, the explicitly correlated CCSD(T)-F12 op-
timized geometric parameters also systematically converge
toward the CBS limit as the cardinal number of the basis
increases.
In agreement with earlier work,37we find that geometric
parameters optimized at the CCSD(T)/CBS limit are in excel-
lent agreement with experiment. For a given cardinal number,
geometric parameters optimized using the explicitly corre-
lated methods are found to be in much better agreement with
CCSD(T)/CBS limit and hence with the experiment than geo-
metric parameters optimized with conventional CCSD(T). In
general, CCSD(T)-F12 geometric parameters obtained with a
given basis set are of comparable accuracy to conventional
CCSD(T) results obtained with a Dunning basis set two car-
dinal numbers higher.
B. Complex geometry
In Fig. 1 we show the optimized geometries of CO2–
Ar, CO2–N2, CO2–CO, CO2–H2O, and CO2–NH3. We find
that the lowest energy structure of all five complexes is
“T-shaped,” with the electron deficient carbon atom of the
CO2 subunit acting as an electron acceptor and the adja-
cent heavy atom of the other subunit acting as an elec-
tron donor. All five complexes and the corresponding six
monomers are uncharged. We determine the magnitude of
charge transfer for each complex from the net difference in
natural atomic charges for the two constituent monomers. At
the CCSD/AVQZ level of theory, we find charge transfer of
0.0031 for CO2–Ar, 0.0005 for CO2–N2, 0.0021 for CO2–CO,
0.0019 for CO2–H2O, and 0.0033 for CO2–NH3. The magni-
tude of charge transfer in all five complexes is small as CO2
is only a weak electron acceptor (weak Lewis acid). For com-
parison, charge transfer in BH3–NH3(a strong electron donor
acceptor complex) is 0.3774, calculated with the same level
of theory.
FIG. 1. CCSD(T)-F12b/VQZ-F12 optimized geometries. From left to right,
top to bottom: CO2–Ar, CO2–N2, CO2–CO, CO2–H2O, and CO2–NH3.
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034301-4K. M. de Lange and J. R. Lane J. Chem. Phys. 134, 034301 (2011)
The CO2–Ar complex has been the subject of several ex-
perimental investigations that have utilized molecular beam
techniques to record spectra in the radio frequency, mi-
crowave, and infrared regions.38–42The potential energy sur-
face and vibrational–rotational spectra have also been in-
vestigated theoretically by several groups, with the most
recent calculations completed with the CCSD(T)/aug-cc-
pVTZ method.43–45The results of all these previous inves-
tigations are pleasingly concordant, with the only minimum
found to be a symmetric “T-shaped” structure of C2vsymme-
try, in agreement with the present work.
The geometry of the CO2–N2 complex has been ex-
perimentally determined as a planar symmetric “T-shaped”
structure of C2v symmetry by rotationally resolved FTIR
spectroscopy using a pulsed molecular beam.46This structure
has also been shown to be consistent with recent matrix isola-
tion FTIR spectra.47The optimized geometry of the CO2–N2
complex has been reported with the MP2/aug-cc-pVDZ
and MP2/6-311+G(d) methods, and the potential energy
surface has been explored using fixed monomer geometries
at the MP4 and CCSD(T) levels of theory.47–49Our present
CCSD(T) and CCSD(T)-F12 calculations are consistent with
these previous investigations and find the global minimum
of CO2–N2to be a planar symmetric “T-shaped” structure of
C2vsymmetry.
The CO2–CO complex is isoelectronic with the CO2–N2
complex. The geometry of CO2–CO has been investigated us-
ing microwave spectroscopy and infrared spectroscopy and
corresponds to a planar symmetric “T-shaped” structure of
C2vsymmetry.50–52The electric dipole moment of the CO2–
CO complex has been experimentally measured, and this is
also consistent with a C2v structure.53The potential energy
surface of CO2–CO has been explored using fixed monomer
geometries at the MP4 and CCSD(T) levels of theory.49Our
present CCSD(T) and CCSD(T)-F12 global minimum struc-
tures are consistent with these earlier experimental and theo-
retical investigations.
The lowest energy structure of CO2–H2O has been de-
termined in a number of experimental investigations to be a
planar symmetric “T-shaped” structure of C2vsymmetry.54–57
However, a recent matrix isolation FTIR experiment has sug-
gested that a second asymmetric tilted Csstructure exists.58
This Csstructure is corroborated by the authors own ab initio
calculations with the MP2/aug-cc-pVTZ method,58by previ-
ous MP2/aug-cc-pVTZ calculations by Danten et al.,59and
by subsequent MP2 triple-ζ calculations by Altmann et al.60
However in contrast, Chaban et al. were unable to identify
the asymmetric tilted Cs structure as a minimum using the
MP2/aug-cc-pVTZ method.61Very recently, the potential en-
ergy surface of CO2–H2O was more thoroughly investigated
with the MP2 method and aug-cc-pVDZ to aug-cc-pVQZ
basis sets using both standard and counterpoise optimiza-
tion schemes.62Makarewicz found that the asymmetric tilted
Csstructure was only a minimum with the standard optimiza-
tion scheme using the aug-cc-pVDZ and aug-cc-pVTZ basis
sets, indicating that this structure is an artefact of basis set su-
perposition error with the MP2 level of theory. This result cor-
roborates earlier CCSD(T) investigations by Garden et al. us-
ing standard and counterpoise optimization schemes with the
aug-cc-pVDZ and aug-cc-pVTZ basis sets.63In the present
work, only the symmetric C2v structure of CO2–H2O was
found to be a minimum with both conventional CCSD(T)
and the AVDZ-AV6Z basis sets and explicitly correlated
CCSD(T)-F12 and the VDZ-F12, VTZ-F12, and VQZ-F12
basis sets. The asymmetric tilted Csstructure was found to be
a first order saddle point in all our CCSD(T) and CCSD(T)-
F12 results and was not considered further.
The CO2–NH3 complex has received surprisingly lit-
tle attention in the literature with only a few experimen-
tal investigations64–66and low level calculations.66–68The
structure has been experimentally determined by matrix iso-
lation FTIR spectroscopy and microwave spectroscopy to
be “T-shaped,” with an assumed symmetric C2v CO2–N
framework.64–66Two staggered structures are possible for
CO2–NH3, corresponding to one of the hydrogen atoms be-
ing either in plane with (Cs symmetry) or perpendicular to
(Cssymmetry) the CO2group. The energetic barrier to con-
vert between these two structures is expected to be very small,
permitting almost free rotation around the sixfold potential
about the principal rotation axis.65Our present CCSD(T) and
CCSD(T)-F12 calculations show that the energy of the in
plane and perpendicular structures is almost degenerate, with
the in plane structure ∼0.1 cm−1lower in energy with all
basis sets. However, both structures appear to be first order
saddle points when the harmonic frequencies are calculated
using numerical gradients, with a single imaginary frequency
corresponding to rotation of the NH3subunit. The harmonic
frequencies of both structures were also calculated using an-
alytical gradients in CFOUR,33and only the in plane structure
was found to be a minimum. This result highlights the diffi-
culty in calculating accurate second order energy derivatives
for flat potential energy surfaces via numerical gradients. For
comparison, we present CCSD(T)/AVTZ harmonic frequen-
cies of all five complexes obtained using both the numerical
and analytical gradients in Table SVIII of the supplementary
material.32
C. Intermolecular distance
In Table II we present the standard and CP optimized
CCSD(T) intermolecular distances of CO2–Ar, CO2–N2,
CO2–CO, CO2–H2O, and CO2–NH3. We limit discussion in
the manuscript to consider only the intermolecular distances
of the complexes, with the full optimized geometries given
in Tables SIX–SXVIII of the supplementary material.32The
accuracy of the intermolecular distance can be considered
a guide to how well a particular ab initio method and ba-
sis set describes the intermolecular interactions between two
monomers in a complex.
Unlike the monomer geometries in Table I, the standard
optimized intermolecular distances do not necessarily sys-
tematically and uniformly converge toward the CBS limit as
the cardinal number of the basis set increases. This apparent
oscillation in some of the intermolecular distances with in-
creasing basis set is attributed to a cancellation of basis set
incompleteness error and basis set superposition error. The
magnitude of BSSE and its effect on intermolecular distances
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034301-5 CCSD(T)-F12 intermolecular interactions J. Chem. Phys. 134, 034301 (2011)
is the largest for small basis sets. Hence, if we exclude the
AVDZ results of CO2–CO and the AVDZ and AVTZ results
of CO2–Ar, we find that the optimized intermolecular dis-
tances of the three more weakly bound complexes (CO2–Ar,
CO2–N2, CO2–CO) progressively shorten and converge to the
CBS limit as the cardinal number of the basis set increases.
For CO2–H2O, the standard optimized intermolecular dis-
tance contracts from AVDZ to AVQZ, lengthens from AVQZ
to AV5Z, and then contracts from AV5Z to the CBS limit. For
CO2–NH3,the oscillationintheoptimized intermolecular dis-
tance is worse still. In contrast, the CP optimized intermolec-
ular distances of all five complexes systematically and uni-
formly converge to the CP corrected CBS limit as the cardinal
number of the basis set increases. It is worth noting that the
CBS limits obtained with the standard and CP corrected 1D
potential energy curves are generally in very good agreement
with each other, with the CP values 0.001–0.002 Å smaller.
Hence, comparison to either the standard CBS limit or the CP
corrected CBS limit yields largely the same conclusions.
The systematic and uniform basis set convergence of the
CP optimized intermolecular distances is clearly more satis-
fying than the sometimes oscillatory basis set convergence of
the standard optimized intermolecular distances. However for
a given basis set, the absolute difference between the CP opti-
mized intermolecular distances and the CP CBS limit is actu-
ally larger than the absolute difference between the standard
optimized intermolecular distance and the CBS limit. For ex-
ample, the average absolute error between the AVDZ CP op-
timized distances and the CP CBS limit is ∼0.14 Å whereas,
the average absolute error between the AVDZ standard opti-
mized distances and the CBS limit is ∼0.013 Å. This perhaps
surprising behavior, whereby CP correction increases the dis-
crepancy with the CBS limit, was also noted in our previous
work on hydrogen bonded complexes,9indicating that this is
a systemic problem with CP correction of CCSD(T) inter-
molecular distances. As expected, the difference between the
TABLE II. CCSD(T) intermolecular distances (in angstrom) for CO2–Ar,
CO2–N2, CO2–CO, CO2–H2O, and CO2–NH3.a
CO2–Ar CO2–N2
CO2–COCO2–H2OCO2–NH3
Standard
AVDZ
AVTZ
AVQZ
AV5Z
AV6Z
CBSb
3.4392
3.4461
3.4208
3.4217
3.4221
3.4224
3.1020
3.1147
3.1169
3.1251
3.1270
3.1293
3.2038
3.1889
3.2080
3.2136
3.2150
3.2167
2.7628
2.7577
2.7557
2.7566
2.7565
2.7562
2.9208
2.9224
2.9181
2.9205
—
2.9193
Counterpoise
AVDZ
AVTZ
AVQZ
AV5Z
CBSc
3.6448
3.5055
3.4504
3.4362
3.4205
3.2494
3.1683
3.1440
3.1354
3.1275
3.3463
3.2535
3.2300
3.2223
3.2146
2.8521
2.7902
2.7681
2.7615
2.7552
3.0254
2.9529
2.9318
—
2.9174
aThe intemolecular distance is between the carbon atom of CO2and the closest atom of
the other monomeric substituent, i.e., RC···Ar, RC···N, RC···C, RC···O, and RC···N.
bExtrapolation to the complete basis set limit utilizes the AV5Z and AV6Z results.
cExtrapolation to the complete basis set limit utilizes counterpoise corrected AV5Z and
AV6Z results.
TABLE III. CCSD(T)-F12 intermolecular distances (in angstrom) for
CO2–Ar, CO2–N2, CO2–CO, CO2–H2O, and CO2–NH3.a
CO2–ArCO2–N2
CO2–COCO2–H2OCO2–NH3
CCSD(T)-F12a
VDZ-F12
VTZ-F12
VQZ-F12
3.4178
3.4205
3.4237
3.1371
3.1296
3.1288
3.2241
3.2157
3.2155
2.7610
2.7578
2.7558
2.9259
2.9197
2.9187
CCSD(T)-F12b
VDZ-F12
VTZ-F12
VQZ-F12
3.4327
3.4251
3.4242
3.1453
3.1319
3.1295
3.2328
3.2184
3.2168
2.7650
2.7590
2.7563
2.9314
2.9216
2.9194
aThe intemolecular distance is between the carbon atom of CO2and the closest atom of
the other monomeric substituent, i.e., RC···Ar, RC···N, RC···C, RC···O, and RC···N.
standard and CP optimized intermolecular distances becomes
smaller as the cardinal number of the basis set increases due
to a decrease in the magnitude of BSSE.
In Table III we present the CCSD(T)-F12a and
CCSD(T)-F12boptimized intermolecular
CO2–Ar, CO2–N2, CO2–CO, CO2–H2O, and CO2–NH3.
Unlike our previous work with hydrogen bonded complexes,9
we find that the CCSD(T)-F12 optimized intermolecular dis-
tances of the present weakly bound electron donor acceptor
complexes systematically converge as the cardinal number of
the basis set increases. With exception of the CCSD(T)-F12a
results for CO2–Ar, we find that the intermolecular distances
become progressively smaller from VDZ-F12 to VQZ-F12. In
general, the explicitly correlated intermolecular distances are
in very good agreement with the CBS limits in Table II. We
find that for a given cardinal number, the CCSD(T)-F12 inter-
molecular distance is in much better agreement with the CBS
limit than the conventional CCSD(T) result obtained either
with or without CP correction. The impressive performance
of the explicitly correlated results is particularly pronounced
for the VTZ-F12 and VQZ-F12 results. For example, the
average absolute error (with respect to the CBS limit) of
the VQZ-F12 intermolecular distances is smaller than the
corresponding error in the conventional CCSD(T)/AV6Z
results.
Overall, we find that the CCSD(T)-F12a intermolecular
distances obtained with the VDZ-F12 and VTZ-F12 basis
sets are in slightly better agreement with the CCSD(T)/CBS
limit than the corresponding CCSD(T)-F12b results. How-
ever, this situation reverses for the VQZ-F12 basis set, where
the CCSD(T)-F12b method appears to slightly outperform the
CCSD(T)-F12a method. The observed relative performance
of the CCSD(T)-F12a and CCSD(T)-F12b methods is consis-
tent with previous investigations.8,9
Comparison of the calculated intermolecular distances
in Table II and Table III to experiment is not trivial. The
calculated intermolecular distance represents the minimum
energy equilibrium structure (Re) and allows all geometric
parameters allowed to relax. In contrast, the experimental in-
termolecular distance corresponds to an effective structure
(R0) that is fitted to rotational constants measured in the vi-
brational ground state (B0), with fixed geometric parame-
ters for the monomeric units.39,46,50,57,65The intermolecular
distancesof
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